The effect of quenched bond disorder on first-order phase transitions

TL;DR

This study uses large-scale Monte Carlo simulations to show that quenched bond disorder transforms a first-order phase transition in the 2D three-color Ashkin-Teller model into an emergent criticality with non-Ising exponents, challenging existing analytical understanding.

Contribution

It provides the first detailed numerical analysis of disorder-induced criticality in the 2D Ashkin-Teller model, revealing non-Ising critical exponents and the non-perturbative nature of the phenomenon.

Findings

Disorder rounds the first-order transition into a continuous one.

Critical exponents vary with disorder strength and coupling.

Critical exponents differ from the Ising universality class.

Abstract

We investigate the effect of quenched bond disorder on the two-dimensional three-color Ashkin-Teller model, which undergoes a first-order phase transition in the absence of impurities. This is one of the simplest and striking models in which quantitative numerical simulations can be carried out to investigate emergent criticality due to disorder rounding of first-order transition. Utilizing extensive cluster Monte Carlo simulations on large lattice sizes of up to $128 \times 128$ spins, each of which is represented by three colors taking values $\pm 1$, we show that the rounding of the first-order phase transition is an emergent criticality. We further calculate the correlation length critical exponent, $\nu$, and the magnetization critical exponent, $\beta$, from finite size scaling analysis. We find that the critical exponents, $\nu$ and $\beta$, change as the strength of disorder or the four-spin coupling varies, and we show that the critical exponents appear not to be in the Ising universality class. We know of no analytical approaches that can explain our non-perturbative results. However our results should inspire further work on this important problem, either numerical or analytical.